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 Izv. Akad. Nauk SSSR Ser. Mat., 1968, Volume 32, Issue 5, Pages 1138–1146 (Mi izv2509)

Some general questions in the theory of the Riemann boundary problem

I. B. Simonenko

Abstract: In this paper we investigate the Riemann boundary problem
$$\Phi^+(t)=G(t)\Phi^-(t)+g(t)$$
for $n$ pairs of functions. The solutions $\Phi^\pm$ are to belong to the classes $E_p^\pm$; the given function g belongs to the class $L_p$ $(1<p<\infty)$. We enlarge the class of coefficients $G$ for which the Noether theory remains valid. In the case $n=1$, $p=2$, necessary and sufficient conditions for Noetherianness are obtained. It is shown that the class of matrix-functions which admit factorization coincides with the class for which the Noether theory is valid. In the case $n=1$ it is shown that one of the defect numbers is zero.

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English version:
Mathematics of the USSR-Izvestiya, 1968, 2:5, 1091–1099

Bibliographic databases:

UDC: 517.9
MSC: 30F20, 30E25, 28B20, 46E30, 47A56, 26B35

Citation: I. B. Simonenko, “Some general questions in the theory of the Riemann boundary problem”, Izv. Akad. Nauk SSSR Ser. Mat., 32:5 (1968), 1138–1146; Math. USSR-Izv., 2:5 (1968), 1091–1099

Citation in format AMSBIB
\Bibitem{Sim68} \by I.~B.~Simonenko \paper Some general questions in the theory of the Riemann boundary problem \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1968 \vol 32 \issue 5 \pages 1138--1146 \mathnet{http://mi.mathnet.ru/izv2509} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=235135} \zmath{https://zbmath.org/?q=an:0165.16703|0186.13601} \transl \jour Math. USSR-Izv. \yr 1968 \vol 2 \issue 5 \pages 1091--1099 \crossref{https://doi.org/10.1070/IM1968v002n05ABEH000706} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. I. M. Spitkovsky, “Some estimates for the partial indices of measurable matrix-valued functions”, Math. USSR-Sb., 39:2 (1981), 207–226
2. G. S. Litvinchuk, I. M. Spitkovsky, “Sharp estimates of defect numbers of a generalized Riemann boundary value problem, factorization of hermitian matrix-valued functions and some problems of approximation by meromorphic functions”, Math. USSR-Sb., 45:2 (1983), 205–224
3. Yu. I. Karlovich, V. G. Kravchenko, “An algebra of singular integral operators with piecewise-continuous coefficients and a piecewise-smooth shift on a composite contour”, Math. USSR-Izv., 23:2 (1984), 307–352
4. S. M. Grudskii, “Singular integral equations and the Riemann boundary value problem with infinite index in the space $L_p(\Gamma,\omega)$”, Math. USSR-Izv., 26:1 (1986), 53–76
5. N. L. Vasilevskii, “On an algebra connected with Toeplitz operators in radial tube domains”, Math. USSR-Izv., 30:1 (1988), 71–88
6. I. M. Spitkovsky, “On a vectorial Riemann boundary value problem with infinite defect numbers, and related factorization of matrix-valued functions”, Math. USSR-Sb., 63:2 (1989), 521–538
7. Yu. I. Karlovich, I. M. Spitkovsky, “Factorization of almost periodic matrix-valued functions and the Noether theory for certain classes of equations of convolution type”, Math. USSR-Izv., 34:2 (1990), 281–316
8. Albrecht Böttcher, Yuri I. Karlovich, “Toeplitz and singular integral operators on Carleson curves with logarithmic whirl points”, Integr equ oper theory, 22:2 (1995), 127
9. I. Feldman, I. Gohberg, N. Krupnik, “On explicit factorization and applications”, Integr equ oper theory, 21:4 (1995), 430
10. L. P. Castro, F.-O. Speck, “On the Characterization of the Intermediate Space in Generalized Factorizations”, Math Nachr, 176:1 (1995), 39
11. A. Böttcher, Yu. I. Karlovich, V. S. Rabinovich, “Emergence, persistence, and disappearance of logarithmic spirals in the spectra of singular integral operators”, Integr equ oper theory, 25:4 (1996), 406
12. Albrecht Böttcher, Yuri I. Karlovich, “Submultpilicative fuctions and spectral theory of toeplitz operators”, Integral Transforms and Special Functions, 4:1-2 (1996), 181
13. A. Yu. Karlovich, “The index of singular integral operators in reflexive Orlicz spaces”, Math. Notes, 64:3 (1998), 330–341
14. M.A. Bastos, Yu.I. Karlovich, A.F. dos Santos, P.M. Tishin, “The Corona Theorem and the Existence of Canonical Factorization of Triangular AP-Matrix Functions”, Journal of Mathematical Analysis and Applications, 223:2 (1998), 494
15. J. A. Ball, Yu. I. Karlovich, L. Rodman, I. M. Spitkovsky, “Sarason interpolation and Toeplitz corona theorem for almost periodic matrix functions”, Integr equ oper theory, 32:3 (1998), 243
16. C. J. Bishop, A. Böttcher, Yu. I. Karlovich, I. Spitkovsky, “Local Spectra and Index of Singular Integral Operators with Piecewise Continuous Coefficients on Composed Curves”, Math Nachr, 206:1 (1999), 5
17. Torsten Ehrhardt, Frank-Olme Speck, “Transformation techniques towards the factorization of non-rational 2×2 matrix functions”, Linear Algebra and its Applications, 353:1-3 (2002), 53
18. M.A. Bastos, Yu.I. Karlovich, A.F. dos Santos, “Oscillatory Riemann–Hilbert problems and the corona theorem”, Journal of Functional Analysis, 197:2 (2003), 347
19. V. V. Simonyan, “On connection of one class of one-dimensional pseudodifferential operators with singular integral operators”, Uch. zapiski EGU, ser. Fizika i Matematika, 2009, no. 2, 8–15
20. Karlovich A.Yu., “Singular Integral Operators on Variable Lebesgue Spaces with Radial Oscillating Weights”, Operator Algebras, Operator Theory and Applications, Operator Theory Advances and Applications, 195, 2010, 185–212
21. Karlovich A.Yu., “Singular Integral Operators on Variable Lebesgue Spaces over Arbitrary Carleson Curves”, Topics in Operator Theory: Operators, Matrices and Analytic Functions, Operator Theory Advances and Applications, 1, 2010, 321–336
22. G. Mishuris, S. Rogosin, “An asymptotic method of factorization of a class of matrix functions”, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 470:2166 (2014), 20140109
23. A. G. Kamalian, I. M. Spitkovsky, “On the Fredholm Property of a Class of Convolution-Type Operators”, Math. Notes, 104:3 (2018), 404–416
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